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Sliding Hockey Puck

  1. Sep 6, 2012 #1
    1. The problem statement, all variables and given/known data
    A hockey puck is sliding across a frozen pond with an initial speed of 7.5 m/s. It comes to rest after sliding a distance of 23.7 m. What is the coefficient of kinetic friction between the puck and the ice?

    v0x = initial speed = 7.5 m/s
    vfx = final speed = 0 m/s
    Δx = x distance traveled = 23.7 m
    fk,IP = force of kinetic friction from ice on puck
    NIP = normal force from ice on puck
    WEP = weight force from earth on puck
    mP = mass of puck
    g = acceleration due to gravity

    2. Relevant equations
    ƩFnet = m*a
    ƩFx = -fk,IP = m*ax
    ƩFy = NIP - WEP = m*ay → ay = 0 m/s^2 → NIP = mP*g

    3. The attempt at a solution
    I attempted this logic...

    fk,IP = μk*NIP → (-m*ax)/(mP*g) = μk

    But then I hit a wall when trying to find the x-acceleration. Help?
     
  2. jcsd
  3. Sep 6, 2012 #2
    You need the equation of distance traveled under constant acceleration (deceleration in this case).
     
  4. Sep 18, 2012 #3
    I am not allowed to have the equations of constant acceleration to solve problems. I must derive all equations myself using calculus. How do I even know that the acceleration is constant?
     
  5. Sep 18, 2012 #4
    there's only one force acting on the puck in the x-direction: the frictional force

    and it depends on two constant values: the coefficient of friction and the normal force on the puck

    therefore, the force is constant, therefore the acceleration is constant

    set up the equation of motion

    [itex]\Sigma F = m\ddot{x} = F_{friction}[/itex]

    and go from there

    I'm assuming that since they want you to derive the equations yourself, that you know how to do a differential equation, right?
     
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